The Complete Differential Game of Active Target Defense

Dynamic Games and Applications, 2018

A novel pursuit-evasion differential game involving three agents is considered. An Attacker missile is pursuing a Target aircraft. The Target aircraft is aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while at the same time the Attacker tries to minimize said distance. A long-range Beyond Visual Range engagement which is in line with current CONcepts of OPeration is envisaged, and it is therefore assumed that the players have simple motion kinematics á la Isaacs. Also, the speed of the Attacker is equal to the speed of the Defender and the latter is interested in point capture. It is also assumed that at all time the Attacker is aware of the Defender's position, i.e., it is a perfect information game. The analytic/closedform solution of the target defense pursuit-evasion differential game delineates the state space region where the Attacker can reach the Target without being intercepted by the Defender, thus disposing of the Game of Kind. The target defense Game of Degree is played in the remaining state space. The analytic solution of the Game of Degree yields the agents' optimal state feedback strategies, that is, the instantaneous heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker at the instant of Electronic supplementary material The online version of this article (

We use some recent developments in Dynamics Programming Method to obtain the complete and theoretically justified solution of a differential game formulated and studied in \cite{CHE} using the Lanchester equation. We use a certain refinement of Cauchy's Method of characteristics for stratified Hamilton-Jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by a pair of admissible feedback strategies. Its optimality, is justified by using of one of the well-known verification theorems as an argument for sufficient optimality conditions. MSC Classification: 49N70 , 49N35 , 49N90 , 91A23 , 49L20 , 34A60

Proceedings of the 17th IFAC World Congress, 2008, 2008

Pursuit-evasion (PE) differential games have recently received much attention in military applications involving adversaries. We extend the PE game problem to a problem of defending target, where the roles of the players are changed. The evader is to attack some fixed target, whereas the pursuer is to defend the target by intercepting the evader. We propose a practical strategy design approach based on the linear quadratic game theory with a receding horizon implementation. We prove the existence of solutions for the Riccati equations associated with games with simple dynamics. Simulation results justify the method.

International Journal of Control, 2020

In this manuscript we formulate the general Target-Attacker-Defender differential game of degree in both its continuous-time and discrete-time turn based variants in n-dimensional euclidean space. In this three-agent engagement, the Attackers goal is to get as close as possible to the Target before collision with the Defender, whilst the Target and Defender coordinate to achieve the opposite. The most general setting for this zero-sum differential game is considered, where the agents move at speeds not necessarily equal, and the Nash equilibrium strategies are proven in the discrete-time turn based variant.

IEEE Transactions on Automatic Control, 2021

In this paper an N-pursuer vs. M-evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends classical differential game theory to simultaneously address weapon assignments and multi-player pursuit-evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players' optimal strategies require the co-design of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is proposed and the Value function of the game is obtained. It is shown that the Value function is continuous, continuously differentiable, and that it satisfies the Hamilton-Jacobi-Isaacs equation-the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of N = M and N > M are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This work provides a foundation to formally analyze complex and high-dimensional conflicts between teams of N pursuers and M evaders by means of differential game theory. This work has been supported in part by AFOSR LRIR No. 18RQCOR036.

Automatica, 2019

Multi-player pursuit-evasion games are crucial for addressing the maneuver decision problem arising in the cooperative control of multi-agent systems. This work addresses a particular pursuit-evasion game with three players, Target, Attacker, and Defender. The Attacker aims to capture the Target, while avoiding being captured by the Defender and the Defender tries to defend the Target from being captured by the Attacker, while trying to capture the Attacker at an opportune moment. A two-pronged pursuit-evasion problem in this game is considered and we focus on two aspects: the cooperation between the Target and Defender and balancing the roles of the Attacker between pursuer and evader. A barrier based on the explicit policy method and geometric analysis method is constructed to separate the whole state space into two disjoint parts that correspond to two winning regions for the Attacker and Target-Defender team. The main contributions of this work are obtaining the players' winning regions and providing a complete game solution by analyzing the optimal strategies and trajectories of the players based on the barrier.

Sensors

This paper presents a succinct review of attempts in the literature to use game theory to model decision-making scenarios relevant to defence applications. Game theory has been proven as a very effective tool in modelling the decision-making processes of intelligent agents, entities, and players. It has been used to model scenarios from diverse fields such as economics, evolutionary biology, and computer science. In defence applications, there is often a need to model and predict the actions of hostile actors, and players who try to evade or out-smart each other. Modelling how the actions of competitive players shape the decision making of each other is the forte of game theory. In past decades, there have been several studies that applied different branches of game theory to model a range of defence-related scenarios. This paper provides a structured review of such attempts, and classifies existing literature in terms of the kind of warfare modelled, the types of games used, and th...

2020 American Control Conference (ACC), 2020

Pursuit and evasion conflicts represent challenging problems with important applications in aerospace and robotics. In pursuit-evasion problems, synthesis of intelligent actions must consider the adversary's potential strategies. Differential game theory provides an adequate framework to analyze possible outcomes of the conflict without assuming particular behaviors by the opponent. This article presents an organized introduction of pursuit-evasion differential games with an overview of recent advances in the area. First, a summary of the seminal work is outlined, highlighting important contributions. Next, more recent results are described by employing a classification based on the number of players: one-pursuer-one-evader, N-pursuers-one-evader, one-pursuer-M-evaders, and N-pursuer-M-evader games. In each scenario, a brief summary of the literature is presented. Finally, two representative pursuit-evasion differential games are studied in detail: the two-cutters and fugitive ship differential game and the active target defense differential game. These problems provide two important applications and, more importantly, they give great insight into the realization of cooperation between friendly agents in order to form a team and defeat the adversary.

Journal of Mathematical Analysis and Applications, 1979

We consider so-called differential games of kind (qualitative games) involving two or more players each of whom possesses a target toward which he wishes to steer the response of a dynamical system that is under the control of all players. Sufficient conditions are derived, which assure termination on a particular player's target. In general, these conditions are constructive in that they permit construction of a winning (terminating) strategy for a player. The theory is illustrated by a pursuit-evasion problem.

2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2009

This paper describes a basic passive vs. aggressive defense model, and analyzes it in terms of defense strategies against an intelligent enemy. In response to varying combinations of passive and aggressive defense, we assume that the enemy can up-or down-regulate recruitment activity. This leads to a differential game formulation of battle scenarios that we analyze for a warfare situation. Specifically, we consider military counterterrorist activities in a civilian population. Simulation results, including uncertainty and sensitivity analyses, are provided to demonstrate the benefits and limitations of the proposed model in terms of understanding army defense plans.